Question

the mean exam score for 45 male high school students is 24.1 and the population standard deviation is 4.5. the mean exam score for 52 female high school students is 21.1 and the population standard deviation is 4.2. at \\( alpha = 0.01 \\), can you reject the claim that male and female high school students have equal exam scores? complete parts (a) through (e).
click here to view page 1 of the standard normal distribution table
click here to view page 2 of the standard normal distribution table
c. male high school students have greater exam scores than female students.
d. male and female high school students have different exam scores.
what are \\( h _ { 0 } \\) and \\( h _ { a } \\)?
a. \\( h _ { 0 } : mu _ { 1 } = mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 }
eq mu _ { 2 } \\)
b. \\( h _ { 0 } : mu _ { 1 } geq mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 } < mu _ { 2 } \\)
c. \\( h _ { 0 } : mu _ { 1 } leq mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 } > mu _ { 2 } \\)
d. \\( h _ { 0 } : mu _ { 1 } > mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 } leq mu _ { 2 } \\)
e. \\( h _ { 0 } : mu _ { 1 } < mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 } geq mu _ { 2 } \\)
f. \\( h _ { 0 } : mu _ { 1 }
eq mu _ { 2 } \\) \\( h _ { a } : mu _ { 1 } = mu _ { 2 } \\)
(b) find the critical value(s) and identify the rejection region(s).
the critical value(s) is/are \\( pm 2.58 \\).
(round to two decimal places as needed. use a comma to separate answers as needed.)
what is/are the rejection region(s)?
a. \\( z < - 1.64 , z > 1.64 \\)
b. \\( z < - 2.33 , z > - 2.33 \\)
c. \\( z > 2.58 \\)
d. \\( z < 1.64 \\)
e. \\( z < - 2.33 \\)
f. \\( z > - 3.08 \\)
g. \\( z < - 2.58 , z > 2.58 \\)
h. \\( z < - 3.08 , z > - 3.08 \\)

Explanation:

Step1: Determine the type of test

Since the claim is about equality of means and the alternative hypothesis is \(H_{a}:\mu_{1}
eq\mu_{2}\), this is a two - tailed test.

Step2: Recall the rule for rejection regions in a two - tailed z - test

For a two - tailed z - test with significance level \(\alpha = 0.01\), the rejection regions are \(z< - z_{\alpha/2}\) and \(z>z_{\alpha/2}\). Given \(z_{\alpha/2}=2.58\) (from standard normal distribution table for \(\alpha/2=0.005\)), the rejection regions are \(z < - 2.58\) and \(z>2.58\).

Answer:

G. \(z < - 2.58,z>2.58\)